Timothy Williamson is a professor of logic at Oxford. He is a principal architect of necessitism, the claim that everything that exists necessarily exists. Ontology is necessary. Things could not have been otherwise. The universe could not have evolved differently.

Necessitism is opposed to the idea of contingency, which denies that necessarily everything that is something is necessarily something. Ontology is contingent. Things could have been otherwise. There is ontological chance in the universe.

Before Marcus, most philosophers limited the necessity of identity to self-identity. Since her work, David Wiggins in 1965 and Saul Kripke in 1971 have suggested there is no contingent identity.

Williamson reads Barcan Marcus as proving that everything is necessarily what it is, everything that exists necessarily exists.

Williamson writes her argument as

The logical arguments for the necessity and permanence of identity are
straightforward, and widely accepted in at least some form. Suppose that
x is identical with y. Therefore, by the indiscernibility of identicals, x is
whatever y is. But y is necessarily identical with y.Therefore x is necessarily
identical with y. By analogous reasoning, x is always identical with y. More
strongly: necessarily always, if x is identical with y then necessarily always x
is identical with y. Of course, we understand 'x' and 'y' here as variables
whose values are simply things, not as standing for definite descriptions such
as 'the winning number' that denote different things with respect to different
circumstances.

(Modal Logic as Metaphysics, pp.25-26)

There is a serious flaw in the reasoning that "x is whatever y is. But y is necessarily identical with y. Therefore x is necessarily
identical with y." Wiggins and Kripke also made this error. The proper reasoning is "x has the same properties as y. But y is necessarily self-identical with y. Therefore x is necessarily self-identical, i.e., with x."

Numerically distinct objects cannot have identical extrinsic external information, the same relations to other objects in their neighborhood, the same positions in space and time, unless they are one and the same object.

Now Barcan Marcus may be correct if she can be understood as talking about a universe of discourse described by first-order logic. As Rudolf Carnap proposed, the first-order object language can be analyzed for truth values of propositional functions in a second-order metalanguage.

Propositions that are perfectly substitutable in quantified modal logic contexts are necessarily identical. But there are no numerically distinct physical objects that are perfectly identical. Information philosophy shows that numerically distinct objects can have a relative identity if their intrinsic internal information is identical.

Information philosophy has established the existence of metaphysical possibility in two ways. The first is quantum mechanical indeterminacy. The second is the increasing information in the cosmological and biological universe. There can be no new information without possibilities, which depend on ontological chance.

Since information philosophy has shown that the increase in information in our universe is a product of chance events – without possibilities there can be no new information created – in our metaphysics, ontology is irreducibly contingent.

In a deterministic universe (one without contingency or possibility), the total information is a constant, there is but one possible future, the evolution of the universe is entirely present at all times.

This might fit well with Williamson's parallel interest in permanentism, which is a form of pre-determinism or pre-destination that fits with some theological views.